Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Jupiter Images Photo Credits Cover, i Jupiter Images; iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo; v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo; vii Dynamics Graphics Group/Creatas/Alamy; viii Digital Vision/PunchStock; ix, x CORBIS; xi Digital Vision/PunchStock; xii Digital Vision/Getty Images; 2–3 Mike Watson Images/CORBIS; Gary Bbouys/AFP/Getty Images; 32 Mark Ransom/ RansomStudios; 59 Rex Stucky/Getty Images; 68–69 Getty Images; 69 Michael Houghton/StudiOhio; 102 Pixtal/SuperStock; 119 JTB Photo Communications, Inc./Alamy; 128–129 David Madison/NewSport/CORBIS; 129 Christopher Stevenson/CORBIS; 141 Getty Images; 148 James Marshall/CORBIS; 156 CORBIS; 170 image100/Alamy; 188 Rubberball/Getty Images; 189 Brand X/JupiterImages Copyright © 2008 by The McGraw-Hill Companies, Inc All rights reserved Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-878203-9 MHID: 0-07-878203-1 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 1A California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication 1B Chapter Division 1B Chapter Integers Volume Fractions and Decimals 2A Chapter Parts of a Whole 2A Chapter Equivalence of Fractions 2B Chapter Operations with Fractions 2B Chapter Positive and Negative Fractions and Decimals Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Volume Ratios, Rates, and Percents 3A Chapter Ratios and Rates 3A Chapter Percents, Fractions, and Decimals 3B Chapter Using Percents 3B Chapter Rates and Proportional Reasoning Volume The Core Processes of Mathematics 4A Chapter Operations and Equality 4A Chapter Math Fundamentals 4B Chapter Math Expressions 4B Chapter Linear Equations 4B Chapter Inequalities Volume Functions and Equations 5A Chapter Patterns and Relationships 5A Chapter Graphing 5B Chapter Proportional Relationships 5B Chapter The Relationship Between Graphs and Functions Volume Measurement 6A Chapter How Measurements Are Made 6A Chapter Length and Area in the Real World 6B Chapter Exact Measures in Geometry 6B Chapter Angles and Circles iii Authors and Consultants AUTHORS Frances Basich Whitney Kathleen M Brown Dixie Dawson Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Math Curriculum Leader Long Beach Unified Long Beach, California Philip Gonsalves Robyn Silbey Kathy Vielhaber Mathematics Coordinator Alameda County Office of Education Hayward, California Math Specialist Montgomery County Public Schools Gaithersburg, Maryland Mathematics Consultant St Louis, Missouri Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Dinah Zike Educational Consultant, Dinah-Might Activities, Inc San Antonio, Texas CONSULTANTS Assessment Donna M Kopenski, Ed.D Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Planning and Support ELL Support and Vocabulary Beatrice Luchin ReLeah Cossett Lent Mathematics Consultant League City, Texas Author/Educational Consultant Alford, Florida iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc CONTRIBUTING AUTHORS California Advisory Board CALIFORNIA ADVISORY BOARD Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Glencoe wishes to thank the following professionals for their invaluable feedback during the development of the program They reviewed the table of contents, the prototype of the Student Study Guide, the prototype of the Teacher Wraparound Edition, and the professional development plan Linda Anderson Cheryl L Avalos Bonnie Awes Kathleen M Brown 4th/5th Grade Teacher Oliveira Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Carol Cronk Audrey M Day Jill Fetters Grant A Fraser, Ph.D Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California Classroom Teacher Rosa Parks Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel Donna M Kopenski, Ed.D Michael A Pease Chuck Podhorsky, Ph.D Mathematics Department Chair Frontier High School Bakersfield, California Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Math Coach Aspire Public Schools Oakland, California Math Director City Heights Educational Collaborative San Diego, California Arthur K Wayman, Ph.D Frances Basich Whitney Mario Borrayo Melissa Bray Professor Emeritus California State University, Long Beach Long Beach, California Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, CA Teacher Rosa Parks Elementary San Diego, California K–8 Math Resource Teacher Modesto City Schools Modesto, California v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo California Reviewers CALIFORNIA REVIEWERS Each California Reviewer reviewed at least two chapters of the Student Study Guides, providing feedback and suggestions for improving the effectiveness of the mathematics instruction Melody McGuire Math Teacher California College Preparatory Academy Oakland, California 6th and 7th Grade Math Teacher McKinleyville Middle School McKinleyville, California Eppie Leamy Chung Monica S Patterson Teacher Modesto City Schools Modesto, California Educator Aspire Public Schools Modesto, California Judy Descoteaux Rechelle Pearlman Mathematics Teacher Thornton Junior High School Fremont, California 4th Grade Teacher Wanda Hirsch Elementary School Tracy, California Paul J Fogarty Armida Picon Mathematics Lead Aspire Public Schools Modesto, California 5th Grade Teacher Mineral King School Visalia, California Lisa Majarian Anthony J Solina Classroom Teacher Cottonwood Creek Elementary Visalia, California Lead Educator Aspire Public Schools Stockton, California vi Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Bobbi Anne Barnowsky Volume 1A Place Value and Basic Number Skills Chapter Counting Chapters 1, 2, and are contained in Volume 1A Chapters 4, 5, and are contained in Volume 1B 1-1 Counting Numbers Less Than 100 1NS1.1 1-2 Whole Numbers Less Than 100 11 Standards Addressed in This Chapter 1NS1.1 Count, read, and write whole numbers to 100 1NS1.1 Progress Check 18 1-3 Equal Expressions 19 1NS1.3 1-4 Number Patterns .25 1NS1.2 Progress Check 32 1-5 Numbers That Make Ten .33 1NS1.4 1-6 Expanded Form for Two-Digit Numbers 39 1NS1.2 Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than () 1NS1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., may be represented as + 4, + 3, + + + 2, 10 - 2, 11 - 3) 1NS1.4 Count and group objects in ones and tens (e.g., three groups of 10 and equals 34, or 30 + 4) 1NS1.4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Progress Check 46 1-7 Use Symbols to Compare Numbers 47 1NS1.2 1-8 Order Whole Numbers Less Than 100 53 1NS1.2 Progress Check 59 Assessment Study Guide .60 Chapter Test .64 Bridal Veil Falls, El Capitan, and Half Dome, Yosemite National Park Standards Practice 66 vii Dynamics Graphics Group/Creatas/Alamy Contents Chapter Place Value Standards Addressed in This Chapter 2-1 Whole Numbers to 1,000 .70 2NS1.1, 2NS1.2 2-2 Round and Compare Whole Numbers Less Than 1,000 77 2NS1.3, 4NS1.3 Progress Check .84 2-3 Whole Numbers Less Than 10,000 .85 3NS1.3, 3NS1.5 2-4 Round and Compare Whole Numbers Less Than 10,000 91 4NS1.2, 4NS1.3 Progress Check .98 2-5 Read and Write Whole Numbers in the Millions .99 4NS1.1 4NS1.2, 4NS1.3 2-7 Order and Compare Numbers to Two Decimal Places 111 4NS1.2, 4NS1.6 Progress Check 119 Assessment 2NS1.2 Use words, models, and expanded forms (e.g., 45 = tens + 5) to represent numbers (to 1,000) 2NS1.3 Order and compare whole numbers to 1,000 by using the symbols 3NS1.3 Identify the place value for each digit in numbers to 10,000 3NS1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6) 4NS1.1 Read and write whole numbers in the millions 4NS1.2 Order and compare whole numbers and decimals to two decimal places 4NS1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand 4NS1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., = 0.5 or 0.50; = = 1.75) 4 Study Guide 120 Chapter Test 124 Standards Practice 126 viii Digital Digital Vision/PunchStock Vision/PunchStock Giant Redwoods, Sequoia National Park Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 2-6 Round and Compare Whole Numbers in the Millions 105 2NS1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit Contents Chapter Addition and Subtraction Standards Addressed in This Chapter 3-1 Addition Facts for to 130 1NS2.1, 1NS2.6, 2NS2.2 3-2 Addition Facts for and 137 1NS2.1, 1NS2.6, 2NS2.2 Progress Check 144 3-3 Addition Facts for and 145 1NS2.1, 1NS2.5, 1NS2.7 3-4 Estimate and Add Greater Numbers 151 2NS2.3, 3NS1.3, 4NS1.3, 4NS3.1 Progress Check 158 3-5 Subtraction Facts for to 159 1NS2.1, 1NS2.5, 1NS2.6 3-6 Subtraction Facts for to 165 1NS2.1, 1NS2.5, 1NS2.6 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Progress Check 172 3-7 Subtract with Zeros .173 2NS1.2, 2NS2.3, 3NS2.1 3-8 Estimate and Subtract Greater Numbers 181 3NS2.1, 4NS3.1 Progress Check 189 Assessment Study Guide 190 Chapter Test 194 1NS2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory 1NS2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference) 1NS2.6 Solve addition and subtraction problems with one- or two-digit numbers (e.g., + 58 = ) 1NS2.7 Find the sum of three one-digit numbers 2NS2.2 Find the sum or difference of two whole numbers up to three digits long 2NS2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers 3NS1.3 Identify the place value for each digit in numbers to 10,000 3NS2.1 Find the sum or difference of two whole numbers between and 10,000 4NS1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers Standards Practice 196 Cacti growing in Baja California Peninsula ix CORBIS Contents Chapter Multiplication 4-1 Introduction to Multiplication 3NS2.2, 4NS4.1 4-2 Multiply with 0, 1, and 10 3NS2.2, 3NS2.4, 3NS2.6 11 Progress Check 18 4-3 Multiply by 3NS2.2, 3NS2.4 19 4-4 Multiply by 3NS2.2, 3NS2.4 25 Progress Check 32 4-5 Multiply by 3NS2.2, 3NS2.4, 4NS3.2 33 4-6 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 39 Progress Check 46 4-7 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 .47 4-8 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 53 Progress Check 60 4-9 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 61 Progress Check 74 4-11 Multiply by 11 and 12 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 75 4-12 Perfect Squares 3NS2.2, 4NS4.1 81 Progress Check 88 Standards Addressed in This Chapter 2NS3.1 Use repeated addition, arrays, and counting by multiples to multiplication 2NS3.3 Know the multiplication tables of 2s, 5s, and 10s (to “times 10”) and commit them to memory 3NS2.2 Memorize to automaticity the multiplication table for numbers between and 10 3NS2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 × = ) 3NS2.6 Understand the special properties of and in multiplication and division 4NS3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results 4NS4.1 Understand that many whole numbers break down in different ways (e.g., 12 = × = × = × × 3) 4-13 Multiply Large Numbers 3NS2.4, 3NS2.6, 4NS3.2 89 Assessment Study Guide 95 Chapter Test 102 Standards Practice .104 x CORBIS Poppy meadow in the Santa Ynez Mountains Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 4-10 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 67 Chapters 1, 2, and are contained in Volume 1A Chapters 4, 5, and are contained in Volume 1B 10 ART A sports-card collector rotates 665 cards in and out of her display collection Recently she purchased an additional 335 cards from an auction If the collector can display 397 cards, how many cards will not be displayed at any given time? Check off each step Understand Plan Solve Check 11 ASTRONOMY Jin completed a school project He estimated the number of galaxies in the universe to be about 6,450 A recent university study found there to be about 10,000 galaxies By how many galaxies did Jin miss in his estimation? 12 The difference in the number of stocks sold by two companies is about 500,000 What are two numbers that might be the number of stocks sold by each company? Estimate each difference Then find the actual difference 13 845 - 749 14 824 - 325 15 809 - 508 16 703 - 209 Find each difference Use expanded form 17 598 - 567 18 803 - 607 19 800,800 - 51,000 20 52,407 - 24,705 186 Chapter Addition and Subtraction Copyright © by The McGraw-Hill Companies, Inc Skills, Concepts, and Problem Solving Estimate each difference Then find the actual difference 21 85,800 - 79,300 22 37,803 - 34,445 23 41,702 - 22,970 24 15,633 - 9,800 25 908,345 - 720,400 26 709,210 - 559,606 Solve Copyright © by The McGraw-Hill Companies, Inc 27 SCHOOL The enrollment at Protem School is shown in the table About how many more students are in grade than in grade 4? Grade Enrollment 2,245 995 843 28 DRAMA The school musical earned $23,569 in ticket sales the first night The second night, it earned $28,440 Did the musical earn more money the first night or the second night? How much more? 29 COMMUNITY SERVICE The cheerleading squad was making food baskets They made 198 baskets The first day, they distributed 68 baskets About how many baskets are left? GO ON Lesson 3-8 Estimate and Subtract Greater Numbers 187 Solve 30 VOTING The number of voters is shown in the table About how many more voters are in Forest than in Dola? Vocabulary Check sentence Dola Number of Voters 202,450 Forest 299,805 Glenville 184,993 Town Write the vocabulary word that completes each 31 The product of a number and any whole number is the of that number 32 A(n) 33 Writing in Math Write two six-digit numbers Estimate the difference between the numbers Find the exact difference Compare how close your estimate is to the answer Is there a way to get your estimate closer to the actual answer? is a number close to an exact value Spiral Review (Lesson 3-2, p 137) 34 FOOD In the cafeteria, 5-dozen egg cartons were divided into cartons holding a half dozen eggs If there are now 10 half-dozen egg cartons, how many eggs are there in those cartons? 35 BOOKS Sam read seven pages on Wednesday and eight pages on Thursday Write an addition expression to show the total number of pages Sam read Then find the sum of the expression A half-dozen eggs is eggs Compare the whole numbers Use the words more or less (Lesson 1-2, p 11) 36 is 38 33 is 188 than than 13 Chapter Addition and Subtraction Rubberball/Getty Images 37 26 is 39 is than 38 than Copyright © by The McGraw-Hill Companies, Inc Solve Chapter Progress Check (Lessons 3-7 and 3-8) Find each difference Use expanded form 263 - 84 309 - 276 111 - 57 672 - 359 Write an expression for each word phrase the difference of ten and a number the difference of a number and eight Copyright © by The McGraw-Hill Companies, Inc Find each difference 798 267 637 578 1,920 984 10 2,368 - 1,875 _ 11 5,005 - 4,376 _ 12 6,543 - 2,928 _ Estimate each difference Then find the actual difference 13 7,329 - 4,861 14 8,661 - 1,751 Solve 15 MOUNTAIN CLIMBING Albert was at the top of a mountain He descended 3,957 feet About how many feet above sea level was Albert after he descended? 16 HOBBIES Mila collects coins She had 2,454 coins in her collection She sold 567 coins How many coins does Mila have left? The mountain that Albert is climbing is 8,208 feet above sea level Lesson 3-8 Estimate and Subtract Greater Numbers Brand X/JupiterImages 189 Chapter Study Guide Vocabulary and Concept Check addend, p 145 Commutative Property of Addition, p 130 Write the vocabulary word that completes each sentence Some words may be used more than once A(n) problem is an answer to an addition A(n) problem is an answer to a subtraction A(n) is the product of that number and any whole number A(n) is a number close to an exact value that indicates about how much A(n) using the same numbers difference, p 159 estimate, p 151 fact family, p 130 Identity Property of Addition, p 130 multiple, p 151 regroup, p 137 sum, p 145 is a group of related facts Write the correct vocabulary term in the blank Lesson Review 3-1 Addition Facts for to (pp 130–136) Find each sum 43 + 51 = 34 + 22 = 214 + 302 = 10 351 + 244 = 11 135 + 153 = 12 1,212 + 3,421 = 190 Chapter Study Guide Example Find the sum of 431 and 121 Write the problem in vertical format Add the ones column Write the sum in the ones column Add the tens column Write the sum in the tens column Add the hundreds column Write the sum in the hundreds column 431 + 121 431 + 121 552 Copyright © by The McGraw-Hill Companies, Inc 3+6=9 6+3=9 9-6=3 9-3=6 3-2 Addition Facts for and Find each sum 13 16 + 36 = 14 36 + 36 = 15 164 + 165 = 16 97 + 86 = 17 437 + 527 = 18 216 + 106 = (pp 137–143) Example Find the sum of 77 and 76 Write in vertical format Add the ones column + = 13 Because 13 is greater than 10, you need to regroup 77 + 76 _ 77 + 76 _ In expanded form, 13 is 10 + Place the ones digit in the ones column and the tens digit in the tens column above the addends Copyright © by The McGraw-Hill Companies, Inc Add the tens column + + = 15 Write the answer to the left of the 3-3 Addition Facts for and Find each sum 19 77 + 76 _ 153 (pp 145–150) Example 28 + 39 = 20 48 + 48 = Use the “make ten” strategy to find the sum of 88 and 98 21 288 + 197 = Write the first number 88 22 49 + 192 = 23 919 + 828 = The next multiple of 10 after 88 is 90 What number plus 88 makes 90? 24 9,132 + 843 = Write the second number as a sum using 2 + 96 = 98 Rewrite the addition problem (88 + 2) + 96 = 90 + 96 = 186 Chapter Study Guide 191 3-4 Estimate and Add Greater Numbers (pp 151–157) Estimate the sum Then find the actual sum 25 478 + 192 26 789 + 901 3-5 Subtraction Facts for to (pp 159–164) Find each difference 25 - 13 = 28 14 - 10 = 29 15 - = 30 54 - 31 = 3-6 Subtraction Facts for to (pp 165–171) Find each difference Estimate the sum of 3,216 and 8,754 Then find the actual sum What is the greatest place value of the numbers? thousands Round the addends to the thousands place 3,000 + 9,000 Estimate the sum 12,000 Calculate the actual sum Compare 12,000 is close to 11,970 The 3,216 answer is reasonable + 8,754 _ 11,970 Example Find the difference of 34 and 12 Write in vertical format Subtract the ones column 34 Subtract the tens column 12 _ Write the difference 22 22 Check using addition 22 + 12 = 34 Example Find the difference of 673 and 135 31 87 - 65 = Write in vertical format 32 66 - 39 = 33 196 - 58 = Subtract Because < 5, you need to regroup 34 541 - 275 = 10 + 673 135 538 10 + = 13 13 - = The difference is 538 Check: 135 + 538 = 673 192 Chapter Study Guide 34 12 _ 673 135 Copyright © by The McGraw-Hill Companies, Inc 27 Example 3-7 Subtract with Zeros (pp 173–180) Example Find each difference 35 102 - 36 = 36 210 - 183 = 37 306 - 118 = 38 903 - 67 = 39 230 - 109 = 40 500 - 355 = Find the difference of 407 and 280 Write the numbers in expanded form 400 + + - (200 + 80 + 0) _ Regroup because < 300 + 100 + - (200 + 80 + 0) Subtract 300 + 100 + - (200 + 80 + 0) 100 + 20 + Write the difference 127 3-8 Estimate and Subtract Larger Numbers (pp 181–187) Copyright © by The McGraw-Hill Companies, Inc Estimate each difference Then find the actual difference Example Estimate the difference of 4,923 and 3,116 Find the actual difference 41 996 - 328 42 557 - 172 Round the numbers to the nearest thousands Estimate the difference 5,000 - 3,000 = 2,000 43 12,465 - 8,296 Subtract Regroup as needed What is the greatest place value of the numbers? thousands 13 4,923 - 3,116 _ 1,807 Compare your answer and estimate 1,807 is close to the estimate, so it is reasonable Chapter Study Guide 193 Chapter Chapter Test Find each sum Then write the commutative fact 4+5 10 11 12 10 11 12 3+1 Use the “make ten” strategy to find each sum 7+4 9+8 8+6 6+7 Find each sum 47 + 18 = 82 + 94 = 356 + 275 = 10 986 + 207 = Find each difference 96 - 53 = 12 71 - 48 = 13 681 - 396 = 14 908 - 263 = Copyright © by The McGraw-Hill Companies, Inc 11 Find each sum Estimate first 15 6,312 + 5,691 16 1,009 + 2,935 Estimate the difference Find the actual difference 17 4,516 - 1,987 18 12,656 - 9,342 GO ON 194 Chapter Test Solve 19 FOOD When Joyce went to the Tree Branch Café, she purchased a soup and salad combination for $6.59, an iced tea for $1.97, and a bagel and cheese spread for $2.49 Estimate the total cost of her bill Then find the actual total cost 20 NUTRITION Kono read the nutritional facts on two frozen meals One meal had 565 Calories The other meal had 780 Calories Exactly how many more Calories did the second meal have? 21 NUMBER SENSE Frida is years younger than her sister Alana How old is Frida when Alana is 17? 22 TRAVEL One day Kelsey rode her bicycle from her house to school After school she rode to karate class After karate she rode to her friend Kyle’s house to borrow a book Finally, Kelsey rode from Kyle’s house back to her house Look at the map to determine how many miles Kelsey rode her bicycle that day Copyright © by The McGraw-Hill Companies, Inc 23 miles School KARATE miles miles miles Kelsey’s house Karate Studio Kyle’s house FINANCE In July, Mr Phelps deposited $150 into his savings account In August, he deposited $75 In September, he deposited $135 He deposited $20 in October What was the total amount of money he deposited from July to October? Correct the mistakes 24 Ramona wanted to buy a new outfit to wear to the school dance The jeans cost $37, the top cost $43, and the shoes cost $29.99 She asked her mom if she could borrow $100 to buy all three items What was wrong with her request? 25 What would have been a more accurate money request by Ramona? Give both an estimated total cost of the outfit, as well as the exact total of the cost of the outfit Chapter Test 195 Chapter Standards Practice Choose the best answer and fill in the corresponding circle on the sheet at right Use mental math to find the sum Find the estimated sum by rounding to the nearest thousands place 23 + 14 = A 17 C 37 B 34 D 55 Jorge bought pounds of bananas, pounds of grapes, and pounds of strawberries How many total pounds of fruit did Jorge buy? pounds 5,098 + 2,764 _ pounds H 18 pounds J 19 pounds Find one number for both boxes that makes the sentence true G 7,900 J 8,900 Which number makes the sentence true? A 77 C 81 B 79 D 89 Tyrone and Rolando collect baseball trading cards Tyrone has 837 cards in his collection Rolando has 659 cards How many more baseball cards does Tyrone have? F 178 cards H 222 cards G 238 cards J 288 cards Which number completes this math sentence? 5□ -□4 19 196 9, - 6, □ _ 2, A C A C B D B D Chapter Standards Practice GO ON Copyright © by The McGraw-Hill Companies, Inc G 13 pounds H 8,000 82 + □ = 161 pounds F 11 pounds F 7,000 Find the estimated difference by rounding to the nearest hundreds place 12 What is the expanded form of 79? F seven groups of 10 + 8,471 2,903 _ G seven groups of 10 + F 5,000 H 5,600 G 5,400 J 6,600 H nine groups of 10 + J nine groups of + ANSWER SHEET Which symbol makes this math sentence true? 53 □ 57 Copyright © by The McGraw-Hill Companies, Inc 10 11 Directions: Fill in the circle of each correct answer A B C D A > C < F G H J B = D + A B C D F G H J A B C D F G H J A B C D F G H J A B C D 10 F G H J 11 A B C D 12 F G H J 8,000 + 500 + = F 8,009 H 8,509 G 8,059 J 8,590 Which number represents the model in standard form? Success Strategy Check your answers by working each problem backward Start with the answer and see if your checking yields the other factors in the given problem A 532 C 253 B 325 D 235 Chapter Standards Practice 197 Index A E M addend, 130, 145 equal, 19, 47 making ten, 33–38 addition whole numbers, 130–136, 137–143, 145–150, 151–157 equation, 19 after, expanded form, 39–45, 70–76, 85–90 manipulatives base-ten blocks, 19, 20, 39, 40, 41, 43, 56, 61, 85, 112, 114, 116, 127, 137, 165, 173, 174, 176, 179, 197 fraction strips, 111 money, 36, 69 ten frame, 33, 34, 35, 46, 62 Algebra and Functions, 19, 33, 173 estimate, 151–157, 181–188 even number, 25 expression, 19–24, 137 Answer sheet, 67, 127, 197 F Assessment, 64–65, 124–125, 194–195 fact family, 130, 159, 165 B fourths, 111 before, greater than, 11, 47–52, 77–83, 91–97, 105–110, 111–118 between, greatest, 53 C Chapter Preview, 3, 69, 129 Chapter Test, 64–65, 124–125, 194–195 Commutative Property of Addition, 33 H halves, 111 I Indentity Property of Addition, 130 increase, 145 compare, 47–52, 77–83, 91–97, 105–110, 111–118 K Correct the Mistakes, 65, 125, 195 Key Concept, 4, 11, 19, 25, 33, 39, 47, 53, 70, 77, 85, 91, 99, 105, 111, 130, 137, 145, 151, 159, 165, 173, 181 counting numbers, 4–10 D decimal point, 111 decrease, 173 difference, 159 digit, 33, 70 198 Index minus, 159 L least, 53 less than, 11, 47–52, 77–83, 91–97, 105–110, 111–118 multiple, 151, 181 N number line, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 34, 35, 37, 45, 47, 50, 52, 53, 55, 58, 60, 61, 62, 63, 64, 70, 71, 73, 75, 77, 78, 79, 80, 82, 84, 90, 91, 92, 94, 96, 129, 130, 131, 133, 136, 138, 139, 141, 143, 144, 150, 159, 160, 161, 164, 167, 172, 180, 194 number pattern, 25–31 number sense, 4, 11, 19, 25, 33, 39, 47, 53, 70, 77, 85, 91, 99, 105, 111, 130, 137, 145, 151, 159, 165, 173, 181 O odd number, 25 order, 7–52, 53–58, 77–83, 91–97, 105–110, 111–118 Copyright © by The McGraw-Hill Companies, Inc California Mathematics Content Standards, 4, 11, 19, 25, 33, 39, 47, 53, 70, 77, 85, 91, 99, 105, 111, 130, 137, 145, 151, 159, 165, 173, 181 million, 99–104 money, 69 G base-ten blocks, 19, 20, 39, 40, 41, 43, 56, 61 Mathematical Reasoning See Step-by-Step Problem Solving P period, 99 place value, 39–45, 47, 53, 70–76, 85–90, 91–97 hundreds, 70 hundred thousands, 99 hundredths, 111 million, 99–104 ones, 39 tenths, 111 tens, 39 ten thousands, 99 thousands, 85 plus, 130, 145 Problem-Solving See Step-byStep Problem Solving Progress Check, 18, 32, 46, 59, 84, 98, 119, 144, 158, 172, 189 Copyright © by The McGraw-Hill Companies, Inc R Real-World Applications age, 10, 51 animals, 154 apartments, 135 art, 150, 185 astronomy, 186 banking, 17, 98 basketball, 23 books, 187 business, 155, 170 celebrations, cell phone, 76 collections, 76 community, 95 community service, 136, 169 computers, 88 construction, 110, 125, 163 cooking, 134, 178 crafts, 36, 38, 142 data file, 157 earth science, 103, 148 entertainment, 10, 143 farms, 178 fashion, 65, 169 finance, 195 finances, 157 fitness, 125, 149 food, 187, 195 games, 84, 97 geography, 103, 104, 108, 141, 180 government, 156 health, 144, 149 hobbies, 15, 36, 46, 90, 143, 158, 163, 172, 189 hockey, 15 homework, 172 jobs, 141 literature, 97 manipulatives, 142, 150, 178 measurement, 22, 23 money, 18, 36, 52, 97, 98, 115, 117 mountain climbing, 189 music, 24, 90, 169, 170 nature, 108 number sense, 24, 57, 96, 179, 180, 195 number theory, 82 numbers, 158 nutrition, 50, 59, 195 oceanography, 110 pets, 59 physics, 102 politics, 187 population, 119 puzzles, 10, 16, 28, 30, 42, 43, 44, 46, 74, 76, 81, 83, 84, 88, 90, 98, 116, 134, 135, 150, 158, 164, 171, 179 reading numbers, 58, 99–104 recipes, 136 safety, 65, 164 sales, 58 scales, 185 school, 10, 50, 56, 110, 117, 155, 158, 186 science, 141 shopping, 24, 83 space, 103 sports, 8, 14, 18, 38, 45, 84, 88, 119, 144, 164 swimming, 56 temperature, 51, 118 transportation, 156 travel, 7, 95, 109, 133, 162, 180, 195 Re flect, 8, 15, 23, 29, 37, 43, 51, 57, 74, 82, 89, 96, 103, 109, 116, 134, 141, 149, 163, 169, 179, 186 regroup, 137, 165, 173 round, 77–83, 91–97, 105–110, 111–118 S Spiral Review, 17, 24, 31, 38, 45, 52, 58, 76, 83, 90, 97, 104, 110, 118, 136, 143, 150, 157, 164, 171, 180, 187 standard form, 39–45, 70–76, 85–90, 99–104 Standards Practice, 66–67, 126–127, 196–197 Step-by-Step Practice, 6, 13, 21, 27, 35, 41, 49, 55, 73, 80, 87, 94, 101, 107, 114, 132, 140, 147, 153, 161, 168, 177, 184 Step-by-Step Problem Solving Practice, 7–8, 14–15, 22–23, 28, 36, 42, 50, 56, 74, 81, 88, 95, 102–103, 108, 115–116, 133–134, 141, 148–149, 154–155, 162–163, 169, 178, 185 Act it out, 22 Draw a graph, 28 Draw a picture, Guess and check, 42, 185 Make a chart, 108 Make a diagram, 95 Make a table, 14, 74, 88, 154 Solve a simpler problem, 50, 102, 133, 141, 148, 169 Use logical reasoning, 81 Use a model, 36, 56 Use a table, 115 Work backward, 162 Write an equation, 178 Study Guide, 60–63, 120–123, 190–193 subtraction whole numbers, 159–164, 165–171, 173–180, 181–188 Success Strategy, 67, 127, 197 sum, 130, 145 Index 199 T two-digit numbers, 39–45 V variable, 137 Vocabulary, 4, 11, 19, 25, 33, 39, 47, 53, 70, 77, 85, 91, 99, 105, 111, 130, 137, 145, 151, 159, 165, 173, 181 Vocabulary Check, 10, 16, 24, 31, 38, 44, 52, 58, 76, 83, 90, 97, 104, 110, 117, 136, 143, 150, 157, 164, 171, 180, 187 W Who is Correct?, 5, 12, 21, 26, 34, 40, 48, 54, 72, 79, 86, 93, 100, 106, 113, 131, 139, 147, 153, 161, 167, 176, 183 whole numbers, 11–17, 70–76, 85–90, 91–97, 99–104, 105–110 word form, 39–45, 70–76, 85–90, 99–104 Writing in Math, 10, 17, 24, 31, 38, 45, 52, 58, 76, 83, 90, 97, 104, 110, 118, 136, 143, 150, 157, 164, 171, 180, 187 Z Vocabulary and Concept Check, 60, 120, 190 zero, 11 Copyright © by The McGraw-Hill Companies, Inc 200 Index ... Math Triumphs Volume 1A California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication... Value and Basic Number Skills Chapter Counting Chapters 1, 2, and are contained in Volume 1A Chapters 4, 5, and are contained in Volume 1B 1-1 Counting Numbers Less Than 100 1NS1.1 1-2 Whole Numbers... include and So the counting numbers between and are 2, 3, and YOUR TURN! Use a number line to graph the counting numbers between 13 and 19 Use a number line to graph the counting numbers between and